A city council consists of six Democrats and seven republicans. If a committee of four people is selected, find the probability of selecting two Democrats and two Republicans.

Answers

Answer 1

Answer:

[tex]\bold{\dfrac{63}{143}}[/tex]

Step-by-step explanation:

Number of Democrats = 6

Number of Republicans = 7

Total number of members = 6+7 = 13

To find:

Probability of selecting two Democrats and two Republicans if 4 members are selected in the committee = ?

Solution:

This is a selection problem.

Total number of ways to select 4 members in the committee out of total 13 = [tex]_{13}C_4 = \dfrac{13\times 12\times 11\times 10}{4\times 3\times 2} = 715[/tex]

Number of ways to select 2 Democrats = [tex]_{6}C_2 = \dfrac{6\times 5}{2} = 15[/tex]

Number of ways to select 2 Republicans = [tex]_{7}C_2 = \dfrac{7\times 6}{2} = 21[/tex]

Number of ways to select 2 Democrats and 2 Republicans = 15 [tex]\times[/tex] 21 = 315

Formula for probability of an event E can be observed as:

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]

Here, required probability:

[tex]\dfrac{315}{715} = \bold{\dfrac{63}{143}}[/tex]


Related Questions

Please help
What is the value of k?

Answers

Answer:

30°

Step-by-step explanation:

k and 30° are vertical angles

Therefore, k = 30°

Which sequence is geometric?
1, 5, 9, 13,
2. 6, 8, 10,
5, 7, 9, 11,
ОО
4. 3. 16. 32

Answers

4.3.16.32 is geometric

write the equation of the line in slope intercept form that passes through (10,21) and (15,36)

Answers

Answer:

y = 3x - 9

Step-by-step explanation:

First, find the slope using rise/run (y2 - y1) / (x2 - x1)

Plug in the points:

(36 - 21) / (15 - 10)

15/5

= 3

Next, plug the slope and a point into the equation y = mx + b to find b (y-int)

y = mx + b

21 = 3(10) + b

21 = 30 + b

-9 = b

Then, plug this into the equation, as well as the slope:

y = 3x - 9

A bank is designing a new branch office and needs to determine how much driveway space to allow for cars waiting for drive-up teller service. How many spaces should be provided to have a 96 percent probability of accommodating all of the waiting cars

Answers

This question is incomplete, the complete question is;

A bank is designing a new branch office and needs to determine how much driveway space to allow for cars waiting for drive-up teller service.

The drive-up service will have three tellers and a single waiting line. At another branch of the bank in a similar setting, the average service time for drive-up tellers is four minutes per customer, and average arrival rate is 36 customers per hour. It is expected that the new bank will have similar characteristics.

How many spaces should be provided to have a 96 percent probability of accommodating all of the waiting cars?

Answer:

Eleven (11) spaces should be provided to have a 96 percent probability of accommodating all of the waiting cars

Step-by-step explanation:

Given that:

the average service time for drive-up tellers is four (4) minutes per customer at each branch

Average number of customers per hour is 36

Therefore for 36 customers,

the branch can give ( 36 / 4 ) = 9, mins each customer

from the question, there is a probability of 96%

so we will calculate on the 9 as mentioned above

96% of 9 = 0.96

0.96 × 9= 8.64

If there are 3 tellers in a single line- , then

8.64 + 3 = 11.64 approximately 11

Therefore Eleven (11) spaces should be provided to have a 96 percent probability of accommodating all of the waiting cars

Which digit is the hundred place in the number of 742.891

Answers

Answer:

7

Step-by-step explanation:

if you meant hundredths it would be 9, but 7 is in the hundreds place

The number 0.14114111411114 . . . is

Answers

Answer:

  irrational

Step-by-step explanation:

Any infinite non-repeating decimal fraction is an irrational number.

A......... divides a two-dimensional shape into two congruent shapes

Answers

Answer:

A diagonal

Step-by-step explanation:

The completion times for a job task range from 10.1 minutes to 19.2 minutes and are thought to be uniformly distributed. What is the probability that it will require between 12.7 and 16.8 minutes to perform the task

Answers

Answer:

The  probability is  [tex]P(12.7 < x < 16.8 ) = 0.45[/tex]

Step-by-step explanation:

From the question we are told that

The completion times for a job task range from 10.1 minutes to 19.2 minutes

Generally given that the completion times is uniformly distributed then  the probability that it will require between 12.7 and 16.8 minutes is mathematically represented as

         [tex]P(12.7 < x < 16.8 ) = \frac{ 16.8 - 12.7}{ 19.2 - 10.1 }[/tex]

          [tex]P(12.7 < x < 16.8 ) = 0.45[/tex]

There are 4 roses in a vase of 13 flowers the rest are daisies what is the ratio of all flowers in the vase to daises

Answers

Answer:

The ratio is 13:9

Step-by-step explanation:

Since the rest of the flowers in the vase are daisies, subtract the 4 roses from the 13 flowers. 13 - 4 = 9

There will be 9 daisies in the vase in total. Then they are asking for you to put the ratio of the total flowers to the daisies.

Total Flower = 13

Daisies = 9

The ratio would be 13 to 9.

The ratio of all flowers in the vase to daises is [tex]13:9[/tex]

Let the flowers be F.Let the daisies be D.

Given the following data:

Number of roses = 4 rosesNumber of flowers = 13 flowers

To determine the ratio of all flowers in the vase to daises:

First of all, we would solve for the number of daisies in the vase of flowers.

[tex]Number\;of\;daisies = 13-4[/tex]

Number of daisies = 9 daisies.

Now, we can find the ratio of all flowers in the vase to daises:

[tex]Ratio = F:D\\\\Ratio = 13:9[/tex]

Read more: https://brainly.com/question/18676621

If f(x) = -3x + 4 and g(x) = 2, solve for the value of x for
which f(x) = g(x) is true.
Ya

Answers

f(x) = g(x)

-3x+4 = g(x) ... f(x) replaced with -3x+4

-3x+4 = 2 .... g(x) replaced with 2

-3x+4-4 = 2-4 .... subtract 4 from both sides

-3x = -2

-3x/(-3) = -2/(-3) .... divide both sides by -3

x = 2/3

Answer: 2/3

15 ‒ 5x = 6x + 3 – 2x

Answers

Answer:

x = 4/3

Step-by-step explanation:

15 - 5x = 6x + 3 - 2x

In this kind of equation, we try to seperate the x's and the numbers.

So we add 5x to both sides and subtract 3 from both sides to seperate these values

15 - 3 - 5x + 5x = 6x + 3 - 3 - 2x + 5x

=> 12 = 9x

=> 12/9 = x

=> 4/3 = x

=> x = 4/3

To check, we can plug this in.

15 - 5(4/3) = 6(4/3) + 3 - 2(4/3)

15 - 20/3 = 24/3 + 3 - 8/3

45/3 - 20/3 = 24/3 + 9/3 - 8/3

25/3 = 25/3

So our answer works.

A certain factory produces and sells 800080008000 cars per month, making a monthly net profit of PPP dollars. They sell each car for nnn dollars and it costs them ccc dollars to produce a single car. Write an equation that relates PPP, nnn, and ccc.

Answers

Answer:

P = 8000*(n -c)

Step-by-step explanation:

Profit is the difference between cost and selling price.

For 8000 cars produced per month, the profit will be:

P = 8000*(n -c)

Solve for m c = amt must be one term

Answers

Rewrite the equation as
a
m
t
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a
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=
c
.
a
m
t
=
c
a
m
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Divide each term by
a
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a
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and simplify.
Tap for more steps...
m
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c
a
t

The independent variable of interest in an ANOVA procedure is called a a. partition. b. factor. c. treatment. d. response.

Answers

Answer:

Option b (factor) is the correct choice.

Step-by-step explanation:

ANOVA would be used to assess whenever there were other statistically representative variations seen between results of two or even more individual (totally unconnected) categories.

Two different kinds of independent variables exist such as:

ActiveReference

If the explanatory variables are such an effective variable otherwise we modify the argument of the variable to test its effect on something like a specific parameter.

Certain solutions don't apply to the specified scenario. So choice B was its perfect method for that.

Assume two independent random samples are available which provide sample proportions. For the first sample assume n1= 100 and x1= 39. For the second sample, assume n2= 100 and x2= 49. Test the null hypothesis that the population proportions are equal versus the alternative hypothesis that the proportions are not equal at the 90% confidence level. Frame the test statistic by subtracting the proportion for population 1 from that for population 2. Pick an appropriate z value, p-value and conclusion. Round your answer to the nearest thousandth.
a) z-value = -1.425 p-value= 0.077 statistically significant
b) z-value = 1.425 p-value= 0.077 not statistically significant
c) z-value = 1.425 p-value= 0.077 statistically significant
d) z-value = -1.425 p-value= 0.1543 not statistically significant

Answers

Answer:a) z-value = -1.425 p-value= 0.077 statistically significant

Step-by-step explanation:

Given the following :

n1 = 100; x1 = 39 ; n2 = 100 ; x2 = 49

Z value for two independent samples can be obtained using the relation :

Z = (p1 - p2) /(√p(1-p)) * (√[(1/n1) + (1/n2)]

Z = -1.425

P-value : using the online p-value calculator at a confidence level of 90% from z score

Obtained p value = 0.077079

The p value is less than 0.1 , hence result is significant at p<0.10

2.123x10^3 I need help fast

Answers

Answer:

2123

Step-by-step explanation:

10^3 is the same as 1000. 2.123 times 1000 is 2123

Translate into a variable expression.
fifteen more than one-half of the square of z

Answers

Answer:

15 +(1/2)X z²

this is your expression plz brainlist me and follow me

Find the missing number in this proportion 10/15=?/21

Answers

Answer:

x = 14

Step-by-step explanation:

Using cross products

10          x

----- = --------------

15             21

10*21 = 15x

210 = 15x

Divide each side by 15

210/15 =x

14 =x

4. Order the numbers from least to greatest.
√5, 5, 2.5. Ja

Answers

Answer:

√5 < 2.5 < 5

Step-by-step explanation:

√5= 2.23

therefore,

√5 < 2.5 < 5

what is 7(3x+5y) simplify .

Answers

Answer:

21x +35y

Step-by-step explanation:

7(3x+5y)

Distribute

21x +35y

Answer:

7(3x + 5y) = 0 (3x * 7 + 5y * 7) = 0 (21x + 35y) = 0 Solving 21x + 35y = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms ...

Step-by-step explanation:

I have to write 20 characters to ask this quesiton

Answers

Answer:

You should check off boxes 1, 2, 5, and 6

Step-by-step explanation:

These are all irrational numbers because their decimal places go on indefinitely.

A man drove 14 mi directly east from his home, made a left turn at an intersection, and then traveled 5 mi north to his place of work. If a road was made directly from his home to his place of work, what would its distance be to the nearest tenth of a mile?

Answers

Answer:

14.9 miles

Step-by-step explanation:

If the road was created, the 3 different roads would form a right triangle where the new road would be the hypotenuse and the other 2 roads would be the legs.

We can use the pythagorean theorem to find the length of the hypotenuse, or the new road:

a² + b² = c²

14² + 5² = c²

221 = c²

14.9 = c

= 14.9 miles

Find the equation of the line that goes through (2,9) and (-1,5) in point-slope form

Answers

Answer:

y-9=4/3(x-2)

Step-by-step explanation:

First, find your slope:

The formula for finding slope is [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex].

Our coordinate point for our x₁ and y₁ values will be (2,9) and our coordinate point for our x₂ and y₂ values will be (-1,5).  Now, let's plug those into our formula:

[tex]m=\frac{5-9}{-1-2}=\frac{-4}{-3}=\frac{4}{3}[/tex]

Your slope is 4/3.

Next, plug in your x₁ and y₁ values in for point-slope form.  The equation in variable form is "y-y₁=m(x-x₁)".  So, plugging in our point (2,9) for x₁ and y₁, we get:

y-9=4/3(x-2)

use pythagorean theorem to find the length of the hypotenuse in the triangle shown below 11 and 60

Answers

Answer: The value of the hypotenuse is 61.

Step-by-step explanation:

So we are given a triangle with two known sides; two legs with values of 11 and 60. We have to use the Pythagorean Theorem to find the value of the hypotenuse.

The Pythagorean Theorem states that, "the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides".

This means that:

a^2 + b^2 = c^2

leg^2 + leg^2 = hypotenuse^2

So just by looking at that, we know that we can just substitute the values in:

11^2 + 60^2 = x^2

121 + 3600 = 3721

sqrt of 3721 = 61

So the hypotenuse value is 61.

PLEASE ANSWER

-It took Clare 30 minutes to walk around the garden at a constant speed. At what speed was she walking?

Answers

Answer:

7.5 speed

Step-by-step explanation:

because there are 4 corner in a garden so we will divide 30 min ÷4

The answer is 7.5 speed

i need alot of help. (ALGEBRA)

Answers

Answer:

Award brainliest to this answer

Step-by-step explanation:

1: Lcm is 210 and GCF is 1

2: Lcm is 12 and Gcf is 3

3: LCM is 352 and Gcf is 4

4:LCM is 840 and Gcf is 1

5: LCM 108 and Gcf is 9

6: Lcm is 660 and Gcf is 1

7: Lcm is 840 and Gcf is 2

8: Lcm is 60 and Gcf is 30

9: Lcm is 1512 and Gcf is 1

10: Lcm is 176 Gcf is 4

11: Lcm is 2030 and Gcf is 1

12: Lcm 116 and Gcf is 2

Also, I'm am rather sure in which the veracity of the entailment that this is algebra is incorrect.

A trader bought 60 article for N25000 and sold them at N6000 per dozen.
(i) find the total profit
(ii) find the percentage profit
(c) Find the principal which amounts to N2736 in 3 1/2 years at 4% simple interest

Answers

Step-by-step explanation:

N6000×5=N30000

1)N30000-N25000=N5000

2)N5000÷N25000×100℅=20℅

Error Analysis The solution shown for the equation is
incorrect. What is the correct solution? What is the error?
-7(2-1) - 21
-14-7-21
- 7 = 35
r-5
The solution is (Type the value of r)

Answers

Answer:

-28

Step-by-step explanation:

-7 (2-1)-21

-7 (2-1)=-7

-7-21=-28

Differentiation formula
y=(4x+6)^9​

Answers

Answer:

y = (4x + 6)^9

dy/dx = d(4x +6)^9/dx

using chain rule

[tex]\frac{d(4x + 6)^9}{d(4x+6}[/tex] X [tex]\frac{d(4x + 6)}{dx}[/tex]

[tex]9(4x + 6)^{8}[/tex] X 4

36(4x + 6)^8

(144x + 216)^8

plzz help me and explain

Answers

Answer:

the area is: 90 square inches

Step-by-step explanation:

Since you use the same amount of material to create the rectangle, that means that the area of a parallelogram has the same formula as the area of a rectangle. That is:

Area of  parallelogram = base x height

In our case: 9 in x 10 in = 90 square inches

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